Which method is efficient is compared to the other for numerical integration?

Out of the following methods for numerical integration which is one is best? I want to to know which of the following involves least amount of calculations. If someone can sort following in the order of increasing/decreasing efficiencies I would be much obliged. These methods are:

Newton-Cotes Integration formula.

The Trapizoidal Rule (Composite form).

Simpson's Rule (Composite form).

Romberg's Integration.

Double Integration.

Thank you!

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Dont use caps unless you want to shout – Ram Feb 7 at 12:15
Anyone else with his/her views? – Taha Taha Feb 7 at 12:34
Yes - the site moderators. Please do not use all caps, it is considered rude here. – Zev Chonoles Feb 7 at 13:45
Ok I will be careful next time. – Taha Taha Feb 7 at 15:10

 Thanks a lot @rlgordonma – Taha Taha Feb 7 at 12:18 @TahaTaha: if you found the answer useful, please accept it so it will appear as such to the community. – Ron Gordon Feb 7 at 14:03 Brother, can you please elaborate it a little more, actually I have exam tomorrow morning and I have a question in my text "Compare the efficiency and characteristics of numerical integration methods" I found a lot online and could not find anything useful. Your answer has helped me quite but I think to be prepared fully I will need more arguments to answer my question carefully. If you can please do this I can mark your answer to be best. It is already quite good. Thanks! – Taha Taha Feb 7 at 14:19 If you want to assign a number to them: The $(m,n)$ Romberg is $O(1/2^{2 (m+1) n})$, trapezoidal rule is $O(1/(N^2))$, Simpson is $O(1/N^5)$ and Newton-Cotes can be pushed to whatever order you like, but keep in mind it is unstable: en.wikipedia.org/wiki/… – Ron Gordon Feb 7 at 14:27 Thank you very much! So nice of you. I have marked your question to be the best! – Taha Taha Feb 7 at 15:10